In an LCR circuit (circuit with inductor, capacitor and resistor), are the following statements always true?
The capacitor voltage always lags the resistor voltage by a phase difference of 90°.
The inductor voltage always leads the resistor voltage by a phase difference of 90°.
The current...
Sorry I should have explained it better. When you rearrange the equation, you get the x and dx on one side, and the y and dy on the other side. Do you have to make each side an integral? E.g. does it have to be ∫x dx = ∫y dy, or can you rearrange to x dx = y dy? If you can, what does the...
If you have a differential equation with variables separated, such as dy/dx = 4x2/3y3, and you rearrange it to 3y3 dy = 4x2 dx, what does the dy/dx mean in this case, and can you even rearrange it like that or must you do this: ∫3y3 dy = ∫4x2 dx ?
I never really understood leibniz notation. I know that dy/dx means differential of y with respect to x, but what do the 'd's mean? How come the second-order differential is d2y/dx2? What does that mean? And what does d/dx mean?
Homework Statement
Solve the equation √(6 + 3√2) = √a + √b, writing a and b in the form a + b√c.
Homework Equations
In the answers they say that a + b = 6, but I cannot see how they can say this.
The Attempt at a Solution
I square both sides, and that is as far as I get:
6 + 3√2 =...
Aha! So the net EMF is what creates a current in a closed circuit or part of a circuit? And the net EMF in this circuit is zero so the current will also be zero?
:D
I'm getting confused with EMF, terminal voltage and internal resistance etc... isn't the 1.5V the EMF, which means that the actual potential rise (terminal voltage) will be less that 1.5V?
If I were to add up the EMFs, I would be assuming no current is flowing.
Homework Statement
What is the current in this circuit:
http://img802.imageshack.us/img802/4646/8ekh.png [Broken]
Homework Equations
All potential differences in a closed portion of a circuit must add to 0.
Terminal Voltage = EMF - I x internal resistance.
The Attempt at a Solution
I do not...
Well I factorise it to this k(k - 16) < 0 then what? I tried dividing both sides by k, then I get k < 16 but how can I divide both sides by k as I don't know if its positive/negative? And how do I get the 0 < k?
But I'm not letting z = a + ib. I am simply trying to find all the pairs of a and b that satisfy the equation (a + bi)2 = 48 + 14i
The way I think of it, is that the expression in brackets (a + bi) is not a complex number, its a number (real, imaginary, or complex) added to another number (real...
Why are a and b assumed to be real? It doesn't say anything about that in the question, and if you substitute the imaginary solutions into the original equation, it works. (e.g. the solution a = i, b = -7i works)
Thank you, that makes it a bit easier.
In the answers for that question, they go from a2 - b2 = 48 to the solutions. It seems they are skipping a lot, so that's why I thought there must be an easier way.
Homework Statement
Find all pairs of values a and b that satisfy (a + bi)2 = 48 + 14i
2. The attempt at a solution
I managed to solve it, but it took a while and I was wondering if there is an easier/quicker way.
What I did was expanded (a + bi)2 into (a2 - b2) + 2abi
From there, I can...
Checking solutions -- textbook wrong about roots?
If I have the equation sqrt(3x + 1) = x - 3 and I need to solve for x, by squaring both sides then solving the resulting quadratic, I get the solutions x = 1, 8
However, since I squared the equation, I need to check if the solutions are...
Yeah, I sometimes wonder whether anyone else even exists, maybe I am imagining the whole world somehow.
Those of you who exist, please raise your hand now :3
How do we know that all we think we know about the universe is correct?
The whole universe could be COMPLETELY different from what we perceive. You might say that you can do experiments which show certain things, but what if the experiment observations fit this picture we have built up, however...
Why would the electrons introduced by the current get entangled to the distant copper bar? The electrons from the current are not necessarily entangled with anything, so no, it wouldn't create entangled electrons "from a spooky distance."
Let's try it and see what happens, shall we?
//#define SPEED_OF_LIGHT 300000000
#define SPEED_OF_LIGHT 278
I'll have to shut down the universe while I update the binaries, sorry for any inconvenience.
I read somewhere that if a particle of antimatter collides with a particle of matter, they annihilate each other.
Maybe this is because of what is happening in the 4th dimension(time). Since antimatter is matter traveling backwards in time, maybe the two particles stop in the 4th dimension...